Question

what is the equation of this line?
$y = \frac{1}{2}x - 3$
$y = -\frac{1}{2}x - 3$
$y = -2x - 3$
$y = 2x - 3$

Explanation:

Step1: Identify y-intercept

The line crosses the y-axis at $(0, -3)$, so $b=-3$.

Step2: Calculate slope

Use two points: $(-3, 0)$ and $(0, -3)$.
Slope $m=\frac{-3-0}{0-(-3)}=\frac{-3}{3}=-1$? No, correct points: use $(-3, 0)$ and $(0, -3)$ → $m=\frac{-3-0}{0 - (-3)}=\frac{-3}{3}=-1$? Wait, no, look at the line: when $x=-3$, $y=0$; when $x=0$, $y=-3$. Wait, another point: $x=-1$, $y=-1$? No, wait the line goes down 2 when x increases 1? No, wait the line crosses x-axis at $(-3,0)$ and y-axis at $(0,-3)$. So slope $m=\frac{\Delta y}{\Delta x}=\frac{-3-0}{0 - (-3)}=\frac{-3}{3}=-1$? No, wait the options have $y=-2x-3$? Wait no, let's check: if $x=-3$, $y=-2*(-3)-3=6-3=3$, no. Wait $y=-\frac{1}{2}x-3$: $x=-3$, $y= 1.5-3=-1.5$, no. Wait $y=\frac{1}{2}x-3$: $x=-3$, $y=-1.5-3=-4.5$, no. Wait wait, I misread the axis: the horizontal axis is y (f(x)), vertical is x? Oh! The vertical axis is x, horizontal is y (f(x)). So the line crosses y-axis (horizontal) at $y=-3$ (x=0), and crosses x-axis (vertical) at $x=0$? No, wait the line crosses horizontal axis (y) at $y=-3$ (when x=0), and when y=0, x=-3? No, no, the labels: right side is f(x) (y-axis, horizontal), vertical is x-axis. So the line passes through $(x=-3, y=0)$ and $(x=0, y=-3)$. Wait no, slope is $\frac{\Delta y}{\Delta x}=\frac{-3-0}{0 - (-3)}=\frac{-3}{3}=-1$? But that's not an option. Wait wait, no: when x increases by 1, y decreases by 2. Let's take x=0, y=-3; x=1, y=-5? No, the line at x=4, y=-11? No, wait the line at x=4, y is -11? No, look at the line: when x=4, the line is at y=-11? No, wait the line crosses x=-3 (vertical) at y=0 (horizontal), and x=0 at y=-3, x=1 at y=-5? Oh! Yes, I see: from x=-3 (y=0) to x=0 (y=-3): $\Delta x=3$, $\Delta y=-6$, so slope $m=\frac{-6}{3}=-2$.

Step3: Write slope-intercept form

Slope-intercept form: $y=mx+b$, where $m=-2$, $b=-3$. So $y=-2x-3$.

Answer:

B. $y = -2x - 3$